EVC_NN.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# EVC for nucleon-nucleon scattering.\n",
    "Here we do tests of eigenvector continuation (EC) for the scattering phase shifts of NN scattering in s waves, based on the Minnesota potential ([NPA, 286, 53 (1977)](https://www.sciencedirect.com/science/article/abs/pii/0375947477900070)). However, the code works for general potentials, local/nonlocal, with or without coulomb, real/complex. Note that for complex potentials, the functions that need to be imported are different from those in this notebook; please look at the notebook for alpha-Pb scattering (`EVC_alpha_Pb.ipynb`).  \n",
    "\n",
    "Figures for the Minnesota model from [arXiv:2007.03635](https://arxiv.org/abs/2007.03635), \"Efficient emulators for scattering using eigenvector continuation\" by R.J. Furnstahl, P.J. Millican, and Xilin Zhang are generated here.\n",
    "\n",
    "\n",
    "#### Table of contents\n",
    "\n",
    "1. [A code for testing the covex hull of  basis points](#convex_hull_code)\n",
    "1. [Set up the output directory](#output_dir)\n",
    "1. [Code for generating results](#main_code)\n",
    "1. [Minnesota potential in s waves WITHOUT coulomb](#Main_calculations)\n",
    "  1. [Set the global parameters and define NN potential](#global_para_setup) \n",
    "  1. [For 1S0 channel](#1S0_channel)\n",
    "     1. [A test of scattering wave function from EC](#test_wf)\n",
    "     1. [A test of scattering phase shifts from EC](#test_ps)\n",
    "     1. [Test EC using a sample of test points in a 2-dim parameter space](#test_EC_2dim)\n",
    "     1. [Test EC using a sample of test points in a 4-dim parameter space](#test_EC_4dim)\n",
    "  1. [For 3S1 channel](#3S1_channel)\n",
    "     1. [Test EC using a sample of test points in a 2-dim parameter space](#test_EC_2dim_3S1)\n",
    "     1. [Test EC using a sample of test points in a 4-dim parameter space](#test_EC_4dim_3S1)\n",
    "1. [Collect the results and make plots for both channels](#plots)     \n",
    "  1. [For 1S0 channel](#plots_1S0)\n",
    "  1. [For 3S1 channel](#plots_3S1)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import numpy as np\n",
    "from scipy.integrate import simps\n",
    "from scipy.optimize import linprog\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from pyDOE import lhs    # https://pythonhosted.org/pyDOE/\n",
    "import pickle\n",
    "\n",
    "# local imports\n",
    "from Constants import * \n",
    "from two_body_pot import two_body_pot,  rmat_ini\n",
    "from evc_two_body import EigenvectorContinuationScattering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A code for testing the convex hull of  basis points. <a id=\"convex_hull_code\"></a>\n",
    "This checks within a parameter space whether a point is inside or outside the convex hull of a given set of basis points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "def in_hull(points, x):\n",
    "    '''points are basis points that define the convex hull,\n",
    "    while x is the pointed to be tested.\n",
    "    '''\n",
    "    n_points = len(points)\n",
    "    n_dim = len(x)\n",
    "    c = np.zeros(n_points)\n",
    "    A = np.r_[points.T,np.ones((1,n_points))]\n",
    "    b = np.r_[x, np.ones(1)]\n",
    "    lp = linprog(c, A_eq=A, b_eq=b)\n",
    "    return lp.success\n",
    "\n",
    "### Test this code\n",
    "n_points = 10000\n",
    "n_dim = 10\n",
    "Z = np.random.rand(n_points,n_dim)\n",
    "x = np.random.rand(n_dim)\n",
    "print(in_hull(Z, x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set up the ouput directory <a id=\"output_dir\"></a>\n",
    "Set up a dictionary to save the calcuation results. The pkl file will be saved in the output directory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "outdir='./Notebook_output/NN_Minnesota/'\n",
    "res_dict={}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code for generating results <a id=\"main_code\"></a>\n",
    "\n",
    "    In the following function, we compute and collect all the results needed for comparing EVC with direct calculations. We loop over the list potential-basis. The inputs are self-explanatory; important ones: `local_pot_func` and `nonlocal_pot_func` both have two arguments: `r` (or `rvec` for nonlocal) and potential parameter vector. Note that the computation time below could have been much shorter, if the overlap integrals (without the parameter coefficients) in $\\Delta\\tilde{U}$ are stored, instead of being computed again and again here.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def collect_results(outdir='./', channel='1S0', nuggetsize=1.e-10,  num_basis_list=range(3,10), \n",
    "                     basis_potpara_array_list=np.array([]), test_potpara_list=np.array([]), \n",
    "                    local_pot_func= lambda r : 0, nonlocal_pot_func=lambda rvec:0 ):\n",
    "    test_pc_list=[ ]\n",
    "    num_test, dim_para=np.shape(test_potpara_list)\n",
    "    for i, test_potpara  in enumerate(test_potpara_list):\n",
    "        if i%10==0: print(f'setting up test potential class list: {i, num_test }')\n",
    "        test_local_pot_func= lambda r : local_pot_func(r, test_potpara)\n",
    "        test_nonlocal_pot_func= lambda rvec : nonlocal_pot_func(rvec, test_potpara)\n",
    "        test_pc = two_body_pot(pot_func=test_nonlocal_pot_func, local_pot_func= test_local_pot_func,\n",
    "                       mu=mu, hbar=hbarc, E_mesh=E_pts, r_c=r_c, r_max=r_max, r_in_mesh_pts=nr, r_out_mesh_pts=nr,\n",
    "                        angL=angL, z_t=z_t, z_p= z_p)   \n",
    "        test_pc_list.append(test_pc)\n",
    "    test_pc_list=np.array(test_pc_list)\n",
    "    \n",
    "    for i, num_basis in enumerate(num_basis_list):\n",
    "        # num_basis is the number of potential-basis\n",
    "        print('looping over basis array: ' + f'{num_basis}')\n",
    "        output_file_prefix=outdir +channel + '_para-dim-' + f'{dim_para}' \\\n",
    "        + '_basis-' + f'{num_basis}'+'_full-sample-' + f'{num_test}' + '_'\n",
    "        # output-file prefix, which is used as key for the result dictionary. \n",
    "        basis_potpara_array = basis_potpara_array_list[i]\n",
    "        testinouthaull= np.apply_along_axis(lambda x : in_hull(basis_potpara_array, x), 1, test_potpara_list) \n",
    "        # testinouthuall: a boolen list of whether the test point is insdie or outside the convex haul of basis points\n",
    "        local_pot_func_array = [(lambda V0var:\n",
    "                             (lambda r : local_pot_func(r, V0var ) ) )(V0val) for V0val in basis_potpara_array ]\n",
    "        nonlocal_pot_func_array = [(lambda V0var:\n",
    "                             (lambda rvec : nonlocal_pot_func(rvec, V0var ) ) )(V0val) for V0val in basis_potpara_array ]\n",
    "        pc_array = [two_body_pot( pot_func=nonlocal_pot_func_array[ii], local_pot_func= local_pot_func, mu=mu, hbar=hbarc, \n",
    "                         E_mesh=E_pts, r_c=r_c, r_max=r_max, r_in_mesh_pts=nr, r_out_mesh_pts=nr,\n",
    "                        angL=angL, z_t=z_t, z_p= z_p)  for ii, local_pot_func  in  enumerate(local_pot_func_array)]       \n",
    "        tau_var_mesh_list= [] \n",
    "        ere_var_mesh_list=[]  \n",
    "        c_vec_mesh_list=[] \n",
    "        lag_mesh_list=[]\n",
    "        delta_tilde_U_condition_mesh_list=[]\n",
    "        test_pc_list_E_mesh_list=[]\n",
    "        test_pc_list_delta_mesh_list=[]\n",
    "        test_pc_list_tau_mesh_list=[]\n",
    "        test_pc_list_ere_mesh_list=[]\n",
    "        for j, test_potpara  in  enumerate(test_potpara_list):\n",
    "            test_local_pot_func= lambda r : local_pot_func(r, test_potpara)\n",
    "            test_nonlocal_pot_func= lambda rvec : nonlocal_pot_func(rvec, test_potpara)\n",
    "            my_evc = EigenvectorContinuationScattering(pc_array) \n",
    "            tau_var_mesh, ere_var_mesh, c_vec_mesh, lag_mesh, delta_tilde_U_condition_mesh = \\\n",
    "            my_evc.find_EVC_scattering(new_pot_func=test_nonlocal_pot_func, new_local_pot_func=test_local_pot_func, \n",
    "                                       pinv=False, nugget=True, cond=nuggetsize)\n",
    "            tau_var_mesh_list.append(tau_var_mesh ) \n",
    "            ere_var_mesh_list.append(ere_var_mesh)\n",
    "            c_vec_mesh_list.append(c_vec_mesh) \n",
    "            lag_mesh_list.append(lag_mesh)\n",
    "            delta_tilde_U_condition_mesh_list.append(delta_tilde_U_condition_mesh)\n",
    "            test_pc_list_E_mesh_list.append(test_pc_list[j].E_mesh)\n",
    "            test_pc_list_delta_mesh_list.append(test_pc_list[j].delta_mesh)\n",
    "            test_pc_list_tau_mesh_list.append(test_pc_list[j].tau_mesh)\n",
    "            test_pc_list_ere_mesh_list.append(test_pc_list[j].ere_mesh)\n",
    "        res_dict[output_file_prefix] = {\"test_potpara_list\":test_potpara_list, \"basis_potpara_array\":basis_potpara_array, \n",
    "                                    \"test_pc_list_E_mesh_list\": np.array(test_pc_list_E_mesh_list), \n",
    "                                    \"test_pc_list_delta_mesh_list\": np.array(test_pc_list_delta_mesh_list), \n",
    "                                    \"test_pc_list_tau_mesh_list\": np.array(test_pc_list_tau_mesh_list), \n",
    "                                    \"test_pc_list_ere_mesh_list\": np.array(test_pc_list_ere_mesh_list),\n",
    "                                    \"testinouthaull\": testinouthaull, \n",
    "                                    \"tau_var_mesh_list\": np.array(tau_var_mesh_list), \n",
    "                                    \"ere_var_mesh_list\": np.array(ere_var_mesh_list),  \n",
    "                                    \"c_vec_mesh_list \": np.array(c_vec_mesh_list) , \"lag_mesh_list\" : np.array(lag_mesh_list), \n",
    "                                    \"delta_tilde_U_condition_mesh_list\" : np.array(delta_tilde_U_condition_mesh_list)}   \n",
    "    return test_pc_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Minnesota potential in s waves WITHOUT coulomb.  <a id=\"Main_calculations\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set the global parameters and define NN potential  <a id=\"global_para_setup\"></a>\n",
    "Note for faster evalulation, set `nr=50`, `r_c=10`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# mu: reduced mass; r_c: the radius beyond which the strong interaction is considered as zero. We choose a large value here;\n",
    "# r_max: the maxium radius that the wave function will be computed; z_p and z_t: charges of projectile and target; \n",
    "# nr: number of Gauss–Legendre mesh points in  0< r < r_c, and the same number of mesh points for  r_c < r < r_max; \n",
    "# angL: partial wave; E_pts: the energy mesh on which the wave functions and phase shifts will be computed. \n",
    "mu=hbarc**2/41.47105/2; r_c=10; r_max = 20; z_p=1; z_t=0 ; nr=50; angL=0;\n",
    "E_pts=np.append(np.linspace(0.1, 20, 50 ), np.linspace(21, 150, 50) ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Best values for the potential parameters. See paper for the details.\n",
    "V0_R_Minn = 200. # in MeV\n",
    "V0_t_Minn = -178. # in MeV\n",
    "V0_s_Minn = -91.85 # in MeV\n",
    "kappa_R_Minn = 1.487 # in fm^{-2}\n",
    "kappa_t_Minn = 0.639 # in fm^{-2}\n",
    "kappa_s_Minn = 0.465 # in fm^{-2}\n",
    "### The following is the Minnestota local potential for two s-wave channels.  \n",
    "def local_pot_NN_Minn(r, channel='1S0', V0_R=V0_R_Minn, V0_t= V0_t_Minn, V0_s= V0_s_Minn, \n",
    "                      kappa_R=kappa_R_Minn, kappa_t=kappa_t_Minn, kappa_s=kappa_s_Minn):\n",
    "    u = 1   # exchange parameter\n",
    "    V0_R_eval = V0_R * np.exp(-kappa_R * r**2)\n",
    "    V0_t_eval = V0_t * np.exp(-kappa_t * r**2)\n",
    "    V0_s_eval = V0_s * np.exp(-kappa_s * r**2)\n",
    "    V_W = u/4.*(2*V0_R_eval + V0_t_eval + V0_s_eval)\n",
    "    V_M = (1.-u/2.)*V0_R_eval + (2.-u)/4.*(V0_t_eval + V0_s_eval)\n",
    "    V_B = u/4.*(V0_t_eval - V0_s_eval)\n",
    "    V_H = (2.-u)/4.*(V0_t_eval - V0_s_eval)\n",
    "    if channel=='1S0':    \n",
    "        value = V_W + V_M - V_B - V_H \n",
    "    elif channel=='3S1': \n",
    "        value = V_W + V_M + V_B + V_H \n",
    "    else: \n",
    "        print('Illegal channel.') \n",
    "    return value "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  For 1S0 channel <a id=\"1S0_channel\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "channel='1S0'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### A test of scattering wave function from EC <a id=\"test_wf\"></a>\n",
    "\n",
    "Let us see how well the wave function is reproduced by the EVC for best parameter value. Here we choose 4 potential basis points in the  $V_{0R}$ and $V_{0s}$ space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "E_test = np.array([50]) # testing energy \n",
    "test_V= np.array([V0_R_Minn, V0_s_Minn] ) # testing potential parameter values for V_0R and V_0s\n",
    "nuggetsize=1.e-10 # nuggest size\n",
    "### set up four potential basis \n",
    "deltaV=100\n",
    "lhstable= np.array([ [- 0.5 ,  -0.5 ] ,  [0 , 1 ],  [1, 0] ,  [1, 1 ] ]  )\n",
    "num_basis=np.shape(lhstable)[0]\n",
    "V0array=np.apply_along_axis(lambda v : np.array( [ V0_R_Minn + (v[0]-0.5)*2*deltaV , V0_s_Minn + (v[1] - 0.5) * 2*deltaV  ] ) , \n",
    "                            1, lhstable) \n",
    "local_pot_func_array = [(lambda V0var:\n",
    "                             (lambda r : local_pot_NN_Minn(r, channel=channel, V0_R=V0var[0], V0_s=V0var[1]) ) )(V0val) \n",
    "                            for V0val in V0array ]\n",
    "### pc_array is an array of potental class instances\n",
    "pc_array = [two_body_pot( local_pot_func= local_pot_func, mu=mu, hbar=hbarc, \n",
    "                         E_mesh=E_test, r_c=r_c, r_max=r_max, r_in_mesh_pts=nr, r_out_mesh_pts=nr,\n",
    "                        angL=angL, z_t=z_t, z_p= z_p)  for  local_pot_func in  local_pot_func_array] \n",
    "### test_local_pot_func is the local potential for the test_V parameter values, for which both exact and EC \n",
    "### calculations of scattering calculations can be carried out.  \n",
    "test_local_pot_func= lambda r : local_pot_NN_Minn(r, channel=channel, V0_R= test_V[0], V0_s=test_V[1])\n",
    "test_pc = two_body_pot( local_pot_func= test_local_pot_func, mu=mu, hbar=hbarc, \n",
    "                         E_mesh=E_test, r_c=r_c, r_max=r_max, r_in_mesh_pts=nr, r_out_mesh_pts=nr,\n",
    "                        angL=angL, z_t=z_t, z_p= z_p) \n",
    "### note in the above, the two_body_pot class has compute_ps option for whether the exact calculation of  phase shift\n",
    "### need to be carried out, which by defaul is true.  \n",
    "my_evc = EigenvectorContinuationScattering(pc_array)  ### set up EC calculation\n",
    "tau_var_mesh, ere_var_mesh, c_vec_mesh, lag_mesh, delta_tilde_U_condition_mesh = \\\n",
    "            my_evc.find_EVC_scattering(new_local_pot_func=test_local_pot_func, pinv=False, nugget=True, cond=nuggetsize)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "### EC estimation of the full wave function for r< r_c. \n",
    "rmesh=pc_array[0].r_in_mesh \n",
    "wf_var_mesh=np.zeros(nr)\n",
    "for iB in range(num_basis):\n",
    "    wf_var_mesh=wf_var_mesh + pc_array[iB].scatt_wf_in_re_mesh[0] *c_vec_mesh[0, iB]\n",
    "### The two_body_pot class has attribute, self.scatt_wf_in_re_mesh, for scatt_wf_in_re_mesh for scattering wave function \n",
    "### in r< r_c, computed on the Gauss-Legendre messh, as stored in the self.r_in_mesh. Note the wave function's 0-dim is the \n",
    "### list of the scattering energy. Here we only have one energy, so we pick up self.scatt_wf_in_re_mesh[0]; its 1-dim is the \n",
    "### list of r mesh."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 244.8x163.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for 1s0 channel\n",
    "channel , dim_para = '1S0', 2 \n",
    "fig, ax = plt.subplots(ncols=1, nrows=1, figsize=(3.4, 3.4*2/3), sharex=True, sharey=True) \n",
    "fig.suptitle('NN'+r' ($^1S_0$)'+' scattering; varying '+r'$V_{0R}$, $V_{0s}$'\n",
    "             , x=0.5, y= 1.03,  fontsize=12)\n",
    "\n",
    "ax.tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax.set_ylabel('u(r) (fm)', fontsize=10)\n",
    "ax.set_xlabel('r (fm)', fontsize=10)\n",
    "ax.set_xlim([0, 6])\n",
    "ax.set_ylim([-2, 1.6])\n",
    "for i in range(3):\n",
    "    ax.plot(rmesh, pc_array[i].scatt_wf_in_re_mesh[0], 'b-.')\n",
    "ax.plot(rmesh, pc_array[3].scatt_wf_in_re_mesh[0], 'b-.', label = 'Basis,')    \n",
    "ax.plot(rmesh, wf_var_mesh, 'k-', label= 'EVC,')\n",
    "ax.plot(rmesh, test_pc.scatt_wf_in_re_mesh[0], 'r--', label= 'Exact')\n",
    "ax.legend(loc='lower left', fontsize=10, ncol=3 , columnspacing=0.5, handlelength=1.5, handletextpad=0.5) \n",
    "ax.text(3, 1,  'E=50 (MeV)', size=10, \n",
    "          bbox=dict(boxstyle=\"round\",  ec='black', fc=(1, 1, 1), alpha=0.5))\n",
    "ax.text(0.2, 1.1,  '(a)', size=12)\n",
    "fig.tight_layout()\n",
    "plt.savefig(outdir+'1S0_'+'scatt_wf_4_basis_E_50MeV.pdf', bbox_inches='tight')  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A test of scattering phase shifts from EC <a id=\"test_ps\"></a>\n",
    "Let us plot the phase shifts associated with parameters used above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "pc_array = [two_body_pot( local_pot_func= local_pot_func, mu=mu, hbar=hbarc, \n",
    "                         E_mesh=E_pts, r_c=r_c, r_max=r_max, r_in_mesh_pts=nr, r_out_mesh_pts=nr,\n",
    "                        angL=angL, z_t=z_t, z_p= z_p)  for  local_pot_func in  local_pot_func_array]\n",
    "test_pc = two_body_pot( local_pot_func= test_local_pot_func, mu=mu, hbar=hbarc, \n",
    "                         E_mesh=E_pts, r_c=r_c, r_max=r_max, r_in_mesh_pts=nr, r_out_mesh_pts=nr,\n",
    "                        angL=angL, z_t=z_t, z_p= z_p) \n",
    "my_evc = EigenvectorContinuationScattering(pc_array) \n",
    "tau_var_mesh, ere_var_mesh, c_vec_mesh, lag_mesh, delta_tilde_U_condition_mesh = \\\n",
    "            my_evc.find_EVC_scattering(new_local_pot_func=test_local_pot_func, pinv=False, nugget=True, cond=nuggetsize)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 244.8x163.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for 1s0 channel\n",
    "channel , dim_para = '1S0', 2 \n",
    "fig, ax = plt.subplots(ncols=1, nrows=1, figsize=(3.4, 3.4*2/3), sharex=True, sharey=True) \n",
    "fig.suptitle('NN'+r' ($^1S_0$)'+'; varying '+r'$V_{0R}$, $V_{0s}$'\n",
    "             , x=0.6, y= 1.03,  fontsize=12)\n",
    "\n",
    "ax.tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax.set_ylabel(r'$\\delta_0$ (degree)', fontsize=10)\n",
    "ax.set_xlabel('E (MeV)', fontsize=10)\n",
    "#ax.set_xlim([0, 6])\n",
    "#ax.set_ylim([-2, 1.6])\n",
    "ax.plot(E_pts, np.arctan2(1, 1/np.tan(pc_array[2].delta_mesh)) *180/np.pi, 'b-.')\n",
    "ax.plot(E_pts, pc_array[0].delta_mesh*180/np.pi, 'b-.')\n",
    "ax.plot(E_pts, pc_array[1].delta_mesh*180/np.pi, 'b-.')\n",
    "ax.plot(E_pts, pc_array[3].delta_mesh*180/np.pi, 'b-.', label = 'Basis,')    \n",
    "ax.plot(E_pts, np.arctan(tau_var_mesh*np.sqrt(2*mu*E_pts)/hbarc)*180/np.pi, 'k-', label= 'EVC')\n",
    "ax.plot(E_pts, test_pc.delta_mesh*180/np.pi, 'r--', label= 'Exact')\n",
    "ax.legend(loc='upper right', fontsize=10, ncol=2 , columnspacing=0.5, handlelength=1.5, handletextpad=0.5) \n",
    "ax.text(10, 140,  '(b)', size=12)\n",
    "fig.tight_layout()\n",
    "plt.savefig(outdir+'1S0_'+'scatt_wf_4_basis_phase_shifts.pdf', bbox_inches='tight')  \n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test EC using a sample of test points in a 2-dim parameter space  <a id=\"test_EC_2dim\"></a>\n",
    "\n",
    "Now let us sample a large number of test-potential points in the  $V_{0R}$ and $V_{0s}$ space, as detailed in the paper. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1S0'"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "channel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "deltaV= 100 # MeV, the plus and minus range of potential-strength's variation\n",
    "num_full=200 # number of test-potential points\n",
    "dim_para=2 # dim of the parameter space \n",
    "nuggetsize=1.e-10\n",
    "np.random.seed(8209)\n",
    "\n",
    "test_potpara_list=np.apply_along_axis(lambda v : np.array( [ V0_R_Minn + (v[0] - 0.5)*2*deltaV  , \n",
    "                                                              V0_s_Minn + (v[1] - 0.5) * 2*deltaV ] ) , \n",
    "                            1,  np.random.rand(num_full, dim_para))  \n",
    "num_basis_list= np.arange(3,10)\n",
    "np.random.seed(754)\n",
    "basis_potpara_array_list= [np.apply_along_axis(lambda v : np.array( [ V0_R_Minn + (v[0]-0.5)*2*deltaV, \n",
    "                                                                    V0_s_Minn + (v[1] - 0.5) * 2*deltaV  ] ) , \n",
    "                            1, lhs(dim_para,num_basis))  for num_basis in num_basis_list]\n",
    "local_pot_func= lambda r, potpara_vec : local_pot_NN_Minn(r, channel=channel, V0_R=potpara_vec[0], V0_s=potpara_vec[1])\n",
    "nonlocal_pot_func= lambda rvec, potpara_vec: 0 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "setting up test potential class list: (0, 200)\n",
      "setting up test potential class list: (10, 200)\n",
      "setting up test potential class list: (20, 200)\n",
      "setting up test potential class list: (30, 200)\n",
      "setting up test potential class list: (40, 200)\n",
      "setting up test potential class list: (50, 200)\n",
      "setting up test potential class list: (60, 200)\n",
      "setting up test potential class list: (70, 200)\n",
      "setting up test potential class list: (80, 200)\n",
      "setting up test potential class list: (90, 200)\n",
      "setting up test potential class list: (100, 200)\n",
      "setting up test potential class list: (110, 200)\n",
      "setting up test potential class list: (120, 200)\n",
      "setting up test potential class list: (130, 200)\n",
      "setting up test potential class list: (140, 200)\n",
      "setting up test potential class list: (150, 200)\n",
      "setting up test potential class list: (160, 200)\n",
      "setting up test potential class list: (170, 200)\n",
      "setting up test potential class list: (180, 200)\n",
      "setting up test potential class list: (190, 200)\n",
      "looping over basis array: 3\n",
      "looping over basis array: 4\n",
      "looping over basis array: 5\n",
      "looping over basis array: 6\n",
      "looping over basis array: 7\n",
      "looping over basis array: 8\n",
      "looping over basis array: 9\n"
     ]
    }
   ],
   "source": [
    "test_pc_list_1s0_2dim = collect_results(outdir=outdir, channel=channel, nuggetsize=nuggetsize, num_basis_list=num_basis_list, \n",
    "                     basis_potpara_array_list=basis_potpara_array_list, test_potpara_list=test_potpara_list, \n",
    "                    local_pot_func= local_pot_func, nonlocal_pot_func=nonlocal_pot_func) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Save the results. Most of the calculation output have been stored in the .pkl file, even including the condition number for $\\Delta\\tilde{U}$ matrix and lagrange multiplier. See the keys of the res_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "### save the results to a file\n",
    "with open(outdir+'res_dict.pkl', 'wb') as output:\n",
    "    pickle.dump(res_dict, output, pickle.HIGHEST_PROTOCOL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test EC using a sample of test points in a 4-dim parameter space <a id=\"test_EC_4dim\"></a>\n",
    "\n",
    "Vary $V_{0R}$, $V_{0s}$, $\\kappa_R$ , $\\kappa_s$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "deltaV= 100 # MeV, the plus and minus range of potential-strength's variation\n",
    "deltawidth_relative=0.5\n",
    "num_full=1000 # number of test-potential points\n",
    "dim_para=4 # dim of the parameter space \n",
    "nuggetsize=1.e-10\n",
    "np.random.seed(98734)\n",
    "\n",
    "test_potpara_list=np.apply_along_axis(lambda v : np.array( [ V0_R_Minn + (v[0] - 0.5)*2*deltaV  , \n",
    "                                                              V0_s_Minn + (v[1] - 0.5) * 2*deltaV , \n",
    "                                                              kappa_R_Minn*( 1 + (v[2] - 0.5)/0.5*deltawidth_relative),\n",
    "                                                            kappa_s_Minn*( 1 + (v[3] - 0.5)/0.5*deltawidth_relative)] ) , \n",
    "                            1,  np.random.rand(num_full, dim_para))   \n",
    "num_basis_list= np.arange(dim_para+1,15)\n",
    "np.random.seed(98687)\n",
    "basis_potpara_array_list= [np.apply_along_axis(lambda v : np.array( [ V0_R_Minn + (v[0] - 0.5)*2*deltaV  , \n",
    "                                                              V0_s_Minn + (v[1] - 0.5) * 2*deltaV , \n",
    "                                                              kappa_R_Minn*( 1 + (v[2] - 0.5)/0.5*deltawidth_relative),\n",
    "                                                            kappa_s_Minn*( 1 + (v[3] - 0.5)/0.5*deltawidth_relative)] ) , \n",
    "                            1,  lhs(dim_para,num_basis))  for num_basis in num_basis_list]\n",
    "\n",
    "local_pot_func= lambda r, potpara_vec : local_pot_NN_Minn(r, channel=channel, V0_R=potpara_vec[0], V0_s=potpara_vec[1], \n",
    "                                                          kappa_R=potpara_vec[2], kappa_s=potpara_vec[3])\n",
    "nonlocal_pot_func= lambda rvec, potpara_vec: 0 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "setting up test potential class list: (0, 1000)\n",
      "setting up test potential class list: (10, 1000)\n",
      "setting up test potential class list: (20, 1000)\n",
      "setting up test potential class list: (30, 1000)\n",
      "setting up test potential class list: (40, 1000)\n",
      "setting up test potential class list: (50, 1000)\n",
      "setting up test potential class list: (60, 1000)\n",
      "setting up test potential class list: (70, 1000)\n",
      "setting up test potential class list: (80, 1000)\n",
      "setting up test potential class list: (90, 1000)\n",
      "setting up test potential class list: (100, 1000)\n",
      "setting up test potential class list: (110, 1000)\n",
      "setting up test potential class list: (120, 1000)\n",
      "setting up test potential class list: (130, 1000)\n",
      "setting up test potential class list: (140, 1000)\n",
      "setting up test potential class list: (150, 1000)\n",
      "setting up test potential class list: (160, 1000)\n",
      "setting up test potential class list: (170, 1000)\n",
      "setting up test potential class list: (180, 1000)\n",
      "setting up test potential class list: (190, 1000)\n",
      "setting up test potential class list: (200, 1000)\n",
      "setting up test potential class list: (210, 1000)\n",
      "setting up test potential class list: (220, 1000)\n",
      "setting up test potential class list: (230, 1000)\n",
      "setting up test potential class list: (240, 1000)\n",
      "setting up test potential class list: (250, 1000)\n",
      "setting up test potential class list: (260, 1000)\n",
      "setting up test potential class list: (270, 1000)\n",
      "setting up test potential class list: (280, 1000)\n",
      "setting up test potential class list: (290, 1000)\n",
      "setting up test potential class list: (300, 1000)\n",
      "setting up test potential class list: (310, 1000)\n",
      "setting up test potential class list: (320, 1000)\n",
      "setting up test potential class list: (330, 1000)\n",
      "setting up test potential class list: (340, 1000)\n",
      "setting up test potential class list: (350, 1000)\n",
      "setting up test potential class list: (360, 1000)\n",
      "setting up test potential class list: (370, 1000)\n",
      "setting up test potential class list: (380, 1000)\n",
      "setting up test potential class list: (390, 1000)\n",
      "setting up test potential class list: (400, 1000)\n",
      "setting up test potential class list: (410, 1000)\n",
      "setting up test potential class list: (420, 1000)\n",
      "setting up test potential class list: (430, 1000)\n",
      "setting up test potential class list: (440, 1000)\n",
      "setting up test potential class list: (450, 1000)\n",
      "setting up test potential class list: (460, 1000)\n",
      "setting up test potential class list: (470, 1000)\n",
      "setting up test potential class list: (480, 1000)\n",
      "setting up test potential class list: (490, 1000)\n",
      "setting up test potential class list: (500, 1000)\n",
      "setting up test potential class list: (510, 1000)\n",
      "setting up test potential class list: (520, 1000)\n",
      "setting up test potential class list: (530, 1000)\n",
      "setting up test potential class list: (540, 1000)\n",
      "setting up test potential class list: (550, 1000)\n",
      "setting up test potential class list: (560, 1000)\n",
      "setting up test potential class list: (570, 1000)\n",
      "setting up test potential class list: (580, 1000)\n",
      "setting up test potential class list: (590, 1000)\n",
      "setting up test potential class list: (600, 1000)\n",
      "setting up test potential class list: (610, 1000)\n",
      "setting up test potential class list: (620, 1000)\n",
      "setting up test potential class list: (630, 1000)\n",
      "setting up test potential class list: (640, 1000)\n",
      "setting up test potential class list: (650, 1000)\n",
      "setting up test potential class list: (660, 1000)\n",
      "setting up test potential class list: (670, 1000)\n",
      "setting up test potential class list: (680, 1000)\n",
      "setting up test potential class list: (690, 1000)\n",
      "setting up test potential class list: (700, 1000)\n",
      "setting up test potential class list: (710, 1000)\n",
      "setting up test potential class list: (720, 1000)\n",
      "setting up test potential class list: (730, 1000)\n",
      "setting up test potential class list: (740, 1000)\n",
      "setting up test potential class list: (750, 1000)\n",
      "setting up test potential class list: (760, 1000)\n",
      "setting up test potential class list: (770, 1000)\n",
      "setting up test potential class list: (780, 1000)\n",
      "setting up test potential class list: (790, 1000)\n",
      "setting up test potential class list: (800, 1000)\n",
      "setting up test potential class list: (810, 1000)\n",
      "setting up test potential class list: (820, 1000)\n",
      "setting up test potential class list: (830, 1000)\n",
      "setting up test potential class list: (840, 1000)\n",
      "setting up test potential class list: (850, 1000)\n",
      "setting up test potential class list: (860, 1000)\n",
      "setting up test potential class list: (870, 1000)\n",
      "setting up test potential class list: (880, 1000)\n",
      "setting up test potential class list: (890, 1000)\n",
      "setting up test potential class list: (900, 1000)\n",
      "setting up test potential class list: (910, 1000)\n",
      "setting up test potential class list: (920, 1000)\n",
      "setting up test potential class list: (930, 1000)\n",
      "setting up test potential class list: (940, 1000)\n",
      "setting up test potential class list: (950, 1000)\n",
      "setting up test potential class list: (960, 1000)\n",
      "setting up test potential class list: (970, 1000)\n",
      "setting up test potential class list: (980, 1000)\n",
      "setting up test potential class list: (990, 1000)\n",
      "looping over basis array: 5\n",
      "looping over basis array: 6\n",
      "looping over basis array: 7\n",
      "looping over basis array: 8\n",
      "looping over basis array: 9\n",
      "looping over basis array: 10\n",
      "looping over basis array: 11\n",
      "looping over basis array: 12\n",
      "looping over basis array: 13\n",
      "looping over basis array: 14\n"
     ]
    }
   ],
   "source": [
    "test_pc_list_1s0_4dim = collect_results(outdir=outdir, channel=channel, nuggetsize=nuggetsize, num_basis_list=num_basis_list, \n",
    "                     basis_potpara_array_list=basis_potpara_array_list, test_potpara_list=test_potpara_list, \n",
    "                    local_pot_func= local_pot_func, nonlocal_pot_func=nonlocal_pot_func) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "### save the results to a file\n",
    "with open(outdir+'res_dict.pkl', 'wb') as output:\n",
    "    pickle.dump(res_dict, output, pickle.HIGHEST_PROTOCOL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### for 3S1 channel <a id=\"3S1_channel\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "channel='3S1'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test EC in a 2-dim parameter space <a id=\"test_EC_2dim_3S1\"></a>\n",
    "\n",
    "Now let us sample a large number of test-potential points in the  $V_{0R}$ and $V_{0t}$ space, as detailed in the paper. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3S1'"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "channel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "deltaV= 100 # MeV, the plus and minus range of potential-strength's variation\n",
    "num_full=200 # number of test-potential points\n",
    "dim_para=2 # dim of the parameter space \n",
    "nuggetsize=1.e-9\n",
    "np.random.seed(3049)\n",
    "\n",
    "test_potpara_list=np.apply_along_axis(lambda v : np.array( [ V0_R_Minn + (v[0] - 0.5)*2*deltaV  , \n",
    "                                                              V0_t_Minn + (v[1] - 0.5) * 2*deltaV ] ) , \n",
    "                            1,  np.random.rand(num_full, dim_para))  \n",
    "num_basis_list= np.arange(3,10)\n",
    "basis_potpara_array_list= [np.apply_along_axis(lambda v : np.array( [ V0_R_Minn + (v[0]-0.5)*2*deltaV, \n",
    "                                                                    V0_t_Minn + (v[1] - 0.5) * 2*deltaV  ] ) , \n",
    "                            1, lhs(dim_para,num_basis))  for num_basis in num_basis_list]\n",
    "local_pot_func= lambda r, potpara_vec : local_pot_NN_Minn(r, channel=channel, V0_R=potpara_vec[0], V0_t=potpara_vec[1])\n",
    "nonlocal_pot_func= lambda rvec, potpara_vec: 0 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "setting up test potential class list: (0, 200)\n",
      "setting up test potential class list: (10, 200)\n",
      "setting up test potential class list: (20, 200)\n",
      "setting up test potential class list: (30, 200)\n",
      "setting up test potential class list: (40, 200)\n",
      "setting up test potential class list: (50, 200)\n",
      "setting up test potential class list: (60, 200)\n",
      "setting up test potential class list: (70, 200)\n",
      "setting up test potential class list: (80, 200)\n",
      "setting up test potential class list: (90, 200)\n",
      "setting up test potential class list: (100, 200)\n",
      "setting up test potential class list: (110, 200)\n",
      "setting up test potential class list: (120, 200)\n",
      "setting up test potential class list: (130, 200)\n",
      "setting up test potential class list: (140, 200)\n",
      "setting up test potential class list: (150, 200)\n",
      "setting up test potential class list: (160, 200)\n",
      "setting up test potential class list: (170, 200)\n",
      "setting up test potential class list: (180, 200)\n",
      "setting up test potential class list: (190, 200)\n",
      "looping over basis array: 3\n",
      "looping over basis array: 4\n",
      "looping over basis array: 5\n",
      "looping over basis array: 6\n",
      "looping over basis array: 7\n",
      "looping over basis array: 8\n",
      "looping over basis array: 9\n"
     ]
    }
   ],
   "source": [
    "test_pc_list_3s1_2dim = collect_results(outdir=outdir, channel=channel, nuggetsize=nuggetsize, num_basis_list=num_basis_list, \n",
    "                     basis_potpara_array_list=basis_potpara_array_list, test_potpara_list=test_potpara_list, \n",
    "                    local_pot_func= local_pot_func, nonlocal_pot_func=nonlocal_pot_func) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "### save the results to a file\n",
    "with open(outdir+'res_dict.pkl', 'wb') as output:\n",
    "    pickle.dump(res_dict, output, pickle.HIGHEST_PROTOCOL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test EC in a 4-dim parameter space <a id=\"test_EC_4dim_3S1\"></a>\n",
    "\n",
    "Now let us scan the 4-dim space in $V_{0R}$, $V_{0t}$, $\\kappa_R$ , $\\kappa_t$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "deltaV= 100 # MeV, the plus and minus range of potential-strength's variation\n",
    "deltawidth_relative=0.5\n",
    "num_full=1000 # number of test-potential points\n",
    "dim_para=4 # dim of the parameter space \n",
    "nuggetsize=1.e-9\n",
    "np.random.seed(997)\n",
    "\n",
    "test_potpara_list=np.apply_along_axis(lambda v : np.array( [ V0_R_Minn + (v[0] - 0.5)*2*deltaV  , \n",
    "                                                              V0_t_Minn + (v[1] - 0.5) * 2*deltaV , \n",
    "                                                              kappa_R_Minn*( 1 + (v[2] - 0.5)/0.5*deltawidth_relative),\n",
    "                                                            kappa_t_Minn*( 1 + (v[3] - 0.5)/0.5*deltawidth_relative)] ) , \n",
    "                            1,  np.random.rand(num_full, dim_para))   \n",
    "num_basis_list= np.arange(dim_para+1,15)\n",
    "np.random.seed(9862)\n",
    "basis_potpara_array_list= [np.apply_along_axis(lambda v : np.array( [ V0_R_Minn + (v[0] - 0.5)*2*deltaV  , \n",
    "                                                              V0_t_Minn + (v[1] - 0.5) * 2*deltaV , \n",
    "                                                              kappa_R_Minn*( 1 + (v[2] - 0.5)/0.5*deltawidth_relative),\n",
    "                                                            kappa_t_Minn*( 1 + (v[3] - 0.5)/0.5*deltawidth_relative)] ) , \n",
    "                            1,  lhs(dim_para,num_basis))  for num_basis in num_basis_list]\n",
    "\n",
    "local_pot_func= lambda r, potpara_vec : local_pot_NN_Minn(r, channel=channel, V0_R=potpara_vec[0], V0_t=potpara_vec[1], \n",
    "                                                          kappa_R=potpara_vec[2], kappa_t=potpara_vec[3])\n",
    "nonlocal_pot_func= lambda rvec, potpara_vec: 0 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "setting up test potential class list: (0, 1000)\n",
      "setting up test potential class list: (10, 1000)\n",
      "setting up test potential class list: (20, 1000)\n",
      "setting up test potential class list: (30, 1000)\n",
      "setting up test potential class list: (40, 1000)\n",
      "setting up test potential class list: (50, 1000)\n",
      "setting up test potential class list: (60, 1000)\n",
      "setting up test potential class list: (70, 1000)\n",
      "setting up test potential class list: (80, 1000)\n",
      "setting up test potential class list: (90, 1000)\n",
      "setting up test potential class list: (100, 1000)\n",
      "setting up test potential class list: (110, 1000)\n",
      "setting up test potential class list: (120, 1000)\n",
      "setting up test potential class list: (130, 1000)\n",
      "setting up test potential class list: (140, 1000)\n",
      "setting up test potential class list: (150, 1000)\n",
      "setting up test potential class list: (160, 1000)\n",
      "setting up test potential class list: (170, 1000)\n",
      "setting up test potential class list: (180, 1000)\n",
      "setting up test potential class list: (190, 1000)\n",
      "setting up test potential class list: (200, 1000)\n",
      "setting up test potential class list: (210, 1000)\n",
      "setting up test potential class list: (220, 1000)\n",
      "setting up test potential class list: (230, 1000)\n",
      "setting up test potential class list: (240, 1000)\n",
      "setting up test potential class list: (250, 1000)\n",
      "setting up test potential class list: (260, 1000)\n",
      "setting up test potential class list: (270, 1000)\n",
      "setting up test potential class list: (280, 1000)\n",
      "setting up test potential class list: (290, 1000)\n",
      "setting up test potential class list: (300, 1000)\n",
      "setting up test potential class list: (310, 1000)\n",
      "setting up test potential class list: (320, 1000)\n",
      "setting up test potential class list: (330, 1000)\n",
      "setting up test potential class list: (340, 1000)\n",
      "setting up test potential class list: (350, 1000)\n",
      "setting up test potential class list: (360, 1000)\n",
      "setting up test potential class list: (370, 1000)\n",
      "setting up test potential class list: (380, 1000)\n",
      "setting up test potential class list: (390, 1000)\n",
      "setting up test potential class list: (400, 1000)\n",
      "setting up test potential class list: (410, 1000)\n",
      "setting up test potential class list: (420, 1000)\n",
      "setting up test potential class list: (430, 1000)\n",
      "setting up test potential class list: (440, 1000)\n",
      "setting up test potential class list: (450, 1000)\n",
      "setting up test potential class list: (460, 1000)\n",
      "setting up test potential class list: (470, 1000)\n",
      "setting up test potential class list: (480, 1000)\n",
      "setting up test potential class list: (490, 1000)\n",
      "setting up test potential class list: (500, 1000)\n",
      "setting up test potential class list: (510, 1000)\n",
      "setting up test potential class list: (520, 1000)\n",
      "setting up test potential class list: (530, 1000)\n",
      "setting up test potential class list: (540, 1000)\n",
      "setting up test potential class list: (550, 1000)\n",
      "setting up test potential class list: (560, 1000)\n",
      "setting up test potential class list: (570, 1000)\n",
      "setting up test potential class list: (580, 1000)\n",
      "setting up test potential class list: (590, 1000)\n",
      "setting up test potential class list: (600, 1000)\n",
      "setting up test potential class list: (610, 1000)\n",
      "setting up test potential class list: (620, 1000)\n",
      "setting up test potential class list: (630, 1000)\n",
      "setting up test potential class list: (640, 1000)\n",
      "setting up test potential class list: (650, 1000)\n",
      "setting up test potential class list: (660, 1000)\n",
      "setting up test potential class list: (670, 1000)\n",
      "setting up test potential class list: (680, 1000)\n",
      "setting up test potential class list: (690, 1000)\n",
      "setting up test potential class list: (700, 1000)\n",
      "setting up test potential class list: (710, 1000)\n",
      "setting up test potential class list: (720, 1000)\n",
      "setting up test potential class list: (730, 1000)\n",
      "setting up test potential class list: (740, 1000)\n",
      "setting up test potential class list: (750, 1000)\n",
      "setting up test potential class list: (760, 1000)\n",
      "setting up test potential class list: (770, 1000)\n",
      "setting up test potential class list: (780, 1000)\n",
      "setting up test potential class list: (790, 1000)\n",
      "setting up test potential class list: (800, 1000)\n",
      "setting up test potential class list: (810, 1000)\n",
      "setting up test potential class list: (820, 1000)\n",
      "setting up test potential class list: (830, 1000)\n",
      "setting up test potential class list: (840, 1000)\n",
      "setting up test potential class list: (850, 1000)\n",
      "setting up test potential class list: (860, 1000)\n",
      "setting up test potential class list: (870, 1000)\n",
      "setting up test potential class list: (880, 1000)\n",
      "setting up test potential class list: (890, 1000)\n",
      "setting up test potential class list: (900, 1000)\n",
      "setting up test potential class list: (910, 1000)\n",
      "setting up test potential class list: (920, 1000)\n",
      "setting up test potential class list: (930, 1000)\n",
      "setting up test potential class list: (940, 1000)\n",
      "setting up test potential class list: (950, 1000)\n",
      "setting up test potential class list: (960, 1000)\n",
      "setting up test potential class list: (970, 1000)\n",
      "setting up test potential class list: (980, 1000)\n",
      "setting up test potential class list: (990, 1000)\n",
      "looping over basis array: 5\n",
      "looping over basis array: 6\n",
      "looping over basis array: 7\n",
      "looping over basis array: 8\n",
      "looping over basis array: 9\n",
      "looping over basis array: 10\n",
      "looping over basis array: 11\n",
      "looping over basis array: 12\n",
      "looping over basis array: 13\n",
      "looping over basis array: 14\n"
     ]
    }
   ],
   "source": [
    "test_pc_list_3s1_4dim = collect_results(outdir=outdir, channel=channel, nuggetsize=nuggetsize, num_basis_list=num_basis_list, \n",
    "                     basis_potpara_array_list=basis_potpara_array_list, test_potpara_list=test_potpara_list, \n",
    "                    local_pot_func= local_pot_func, nonlocal_pot_func=nonlocal_pot_func) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "### save the results to a file\n",
    "with open(outdir+'res_dict.pkl', 'wb') as output:\n",
    "    pickle.dump(res_dict, output, pickle.HIGHEST_PROTOCOL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Collect the results and make plots for both channels <a id=\"plots\"></a>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(outdir+'res_dict.pkl', 'rb') as output:\n",
    "    res_dict=pickle.load(output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For 1S0 channel <a id=\"plots_1S0\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 489.6x163.2 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for 1s0 channel in 2-dim space\n",
    "channel , dim_para,  num_full = '1S0', 2, 200 \n",
    "color_list= ['red', 'blue', 'black']  \n",
    "linestyle_list= ['--', '-', ':']\n",
    "fig, ax = plt.subplots(ncols=2, nrows=1, figsize=(3.4*2, 3.4 *2/3), sharex=False, sharey=True) \n",
    "fig.suptitle('NN'+r' ($^1S_0$)'+' scattering; varying '+r'$V_{0R}$, $V_{0s}$' , x=0.5, y= 1.03,  fontsize=12)\n",
    "\n",
    "ax[0].set_yscale('log')\n",
    "ax[0].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[0].set_title('Interpolation', fontsize= 10)\n",
    "ax[0].set_ylabel('Mean of |Relative error|', fontsize=10)\n",
    "ax[1].set_yscale('log')\n",
    "ax[1].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[1].set_title('Extrapolation', fontsize= 10)\n",
    "ax[0].set_xlabel('E (MeV)', fontsize=10)\n",
    "ax[1].set_xlabel('E (MeV)', fontsize=10)\n",
    "########### with num_basis = [4, 6, 8] \n",
    "for i, num_basis  in enumerate([4,6,8]) :  \n",
    "    output_file_prefix=outdir + channel + '_para-dim-' + f'{dim_para}' \\\n",
    "    + '_basis-' + f'{num_basis}'+'_full-sample-' + f'{num_full}' + '_'\n",
    "    test_pc_list_ere_mesh_list, testinouthaull, ere_var_mesh_list  = \\\n",
    "                        map(res_dict[output_file_prefix].get, [ 'test_pc_list_ere_mesh_list', 'testinouthaull', 'ere_var_mesh_list'] )   \n",
    "    ere_mesh_list_1 = test_pc_list_ere_mesh_list[testinouthaull]\n",
    "    ere_mesh_list_2 = test_pc_list_ere_mesh_list[np.logical_not(testinouthaull)]\n",
    "    ere_var_mesh_list_1=ere_var_mesh_list[testinouthaull]\n",
    "    ere_var_mesh_list_2=ere_var_mesh_list[np.logical_not(testinouthaull)]    \n",
    "    ax[0].plot(E_pts, np.mean( np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_1[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_1) ]) , axis=0 ), label = r\"$N_b:$\"+f'{num_basis}', \n",
    "               color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[1].plot(E_pts, np.mean( np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_2[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_2) ]) , axis=0 ), label = r\"$N_b:$\"+f'{num_basis}',\n",
    "              color=color_list[i], linestyle=linestyle_list[i])\n",
    "ax[0].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[1].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "fig.tight_layout()\n",
    "plt.savefig(outdir+'1S0_'+'interpolation_vs_extrapolation_rel_error_paper.pdf', bbox_inches='tight')  \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 489.6x163.2 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for 1s0 channel in 4-dim space\n",
    "channel , dim_para,  num_full = '1S0', 4, 1000 \n",
    "color_list= ['red', 'blue', 'black']  \n",
    "linestyle_list= ['--', '-', ':']\n",
    "fig, ax = plt.subplots(ncols=2, nrows=1, figsize=(3.4*2, 3.4*2/3), sharex=True, sharey=True) \n",
    "fig.suptitle('NN'+r' ($^1S_0$)'+' scattering; varying '+r'$V_{0R}$, $V_{0s}$, $\\kappa_R$, $\\kappa_s$'\n",
    "             , x=0.5, y= 1.03,  fontsize=12)\n",
    "\n",
    "ax[0].set_yscale('log')\n",
    "ax[0].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[0].set_title('Interpolation', fontsize= 10)\n",
    "ax[0].set_ylabel('Mean of |Relative error|', fontsize=10)\n",
    "ax[1].set_yscale('log')\n",
    "ax[1].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[1].set_title('Extrapolation', fontsize= 10)\n",
    "ax[0].set_xlabel('E (MeV)', fontsize=10)\n",
    "ax[1].set_xlabel('E (MeV)', fontsize=10)\n",
    "########### with num_basis = [6, 10, 14] \n",
    "for i, num_basis  in enumerate([6, 10, 14]) :  \n",
    "    output_file_prefix=outdir + channel + '_para-dim-' + f'{dim_para}' \\\n",
    "    + '_basis-' + f'{num_basis}'+'_full-sample-' + f'{num_full}' + '_'\n",
    "    test_pc_list_ere_mesh_list, testinouthaull, ere_var_mesh_list  = \\\n",
    "                        map(res_dict[output_file_prefix].get, [ 'test_pc_list_ere_mesh_list', 'testinouthaull', 'ere_var_mesh_list'] )   \n",
    "    ere_mesh_list_1 = test_pc_list_ere_mesh_list[testinouthaull]\n",
    "    ere_mesh_list_2 = test_pc_list_ere_mesh_list[np.logical_not(testinouthaull)]\n",
    "    ere_var_mesh_list_1=ere_var_mesh_list[testinouthaull]\n",
    "    ere_var_mesh_list_2=ere_var_mesh_list[np.logical_not(testinouthaull)]    \n",
    "    ax[0].plot(E_pts, np.mean( np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_1[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_1) ]) , axis=0 ), label = r\"$N_b:$\"+f'{num_basis}',\n",
    "              color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[1].plot(E_pts, np.mean( np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_2[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_2) ]) , axis=0 ), label = r\"$N_b:$\"+f'{num_basis}', \n",
    "              color=color_list[i], linestyle=linestyle_list[i])\n",
    "ax[0].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[1].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "fig.tight_layout()\n",
    "plt.savefig(outdir+'1S0_'+'interpolation_vs_extrapolation_rel_error_4dim_paper.pdf', bbox_inches='tight')  \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 489.6x326.4 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for 1s0 channel in 2-dim space with more results\n",
    "channel , dim_para,  num_full = '1S0', 2, 200 \n",
    "color_list= ['red', 'blue', 'black']  \n",
    "linestyle_list= ['--', '-', ':']\n",
    "fig, ax = plt.subplots(ncols=2, nrows=2, figsize=(3.4*2, 3.4*2*2/3), sharex=True, sharey=True) \n",
    "fig.suptitle('Relative error for NN'+r' ($^1S_0$)'+' scattering; varying '+r'$V_{0R}$, $V_{0s}$' , x=0.5, y= 1.02,  fontsize=12)\n",
    "\n",
    "\n",
    "ax[0,0].set_yscale('log')\n",
    "ax[0,0].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[0,0].set_title('Mean for interpolation', fontsize= 10)\n",
    "ax[0,1].set_yscale('log')\n",
    "ax[0,1].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[0,1].set_title('Mean for extrapolation', fontsize= 10)\n",
    "ax[1,0].set_yscale('log')\n",
    "ax[1,0].set_xlabel('E (MeV)', fontsize=10)\n",
    "ax[1,0].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[1,0].set_title('Std for interpolation', fontsize= 10)\n",
    "ax[1,1].set_yscale('log')\n",
    "ax[1,1].set_xlabel('E (MeV)', fontsize=10)\n",
    "ax[1,1].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[1,1].set_title('Std for extrapolation', fontsize= 10)\n",
    "########### with num_basis = [4, 6, 8] \n",
    "for i, num_basis  in enumerate([4,6,8]) :  \n",
    "    output_file_prefix=outdir + channel + '_para-dim-' + f'{dim_para}' \\\n",
    "    + '_basis-' + f'{num_basis}'+'_full-sample-' + f'{num_full}' + '_'\n",
    "    test_pc_list_ere_mesh_list, testinouthaull, ere_var_mesh_list  = \\\n",
    "                        map(res_dict[output_file_prefix].get, [ 'test_pc_list_ere_mesh_list', 'testinouthaull', 'ere_var_mesh_list'] )   \n",
    "    ere_mesh_list_1 = test_pc_list_ere_mesh_list[testinouthaull]\n",
    "    ere_mesh_list_2 = test_pc_list_ere_mesh_list[np.logical_not(testinouthaull)]\n",
    "    ere_var_mesh_list_1=ere_var_mesh_list[testinouthaull]\n",
    "    ere_var_mesh_list_2=ere_var_mesh_list[np.logical_not(testinouthaull)]    \n",
    "    ax[0,0].plot(E_pts, np.mean( np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_1[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_1) ]) , axis=0 ), label = r\"$N_b:$\"+f'{num_basis}', \n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[0,1].plot(E_pts, np.mean( np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_2[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_2) ]) , axis=0 ), label = r\"$N_b:$\"+f'{num_basis}',\n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[1,0].plot(E_pts, np.std(np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_1[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_1) ]) , axis=0 ),  label = r\"$N_b:$\"+f'{num_basis}',\n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[1,1].plot(E_pts, np.std(np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_2[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_2) ]) , axis=0 ),  label = r\"$N_b:$\"+f'{num_basis}' , \n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "ax[0,0].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[0,1].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[1,0].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[1,1].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "fig.tight_layout()\n",
    "plt.savefig(outdir+'1S0_'+'interpolation_vs_extrapolation_rel_error.pdf', bbox_inches='tight')  \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 489.6x326.4 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for 1s0 channel in 4-dim with more results\n",
    "channel , dim_para,  num_full = '1S0', 4, 1000 \n",
    "color_list= ['red', 'blue', 'black']  \n",
    "linestyle_list= ['--', '-', ':']\n",
    "fig, ax = plt.subplots(ncols=2, nrows=2, figsize=(3.4*2, 3.4*2*2/3), sharex=True, sharey=True) \n",
    "fig.suptitle('Relative error for NN'+r' ($^1S_0$)'+' scattering; varying '+r'$V_{0R}$, $V_{0s}$, $\\kappa_R$, $\\kappa_s$'\n",
    "             , x=0.5, y= 1.02,  fontsize=12)\n",
    "\n",
    "ax[0,0].set_yscale('log')\n",
    "ax[0,0].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[0,0].set_title('Mean for interpolation', fontsize= 10)\n",
    "ax[0,1].set_yscale('log')\n",
    "ax[0,1].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[0,1].set_title('Mean for extrapolation', fontsize= 10)\n",
    "ax[1,0].set_yscale('log')\n",
    "ax[1,0].set_xlabel('E (MeV)', fontsize=10)\n",
    "ax[1,0].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[1,0].set_title('Std for interpolation', fontsize= 10)\n",
    "ax[1,1].set_yscale('log')\n",
    "ax[1,1].set_xlabel('E (MeV)', fontsize=10)\n",
    "ax[1,1].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[1,1].set_title('Std for extrapolation', fontsize= 10)\n",
    "########### with num_basis = [6, 9, 12] \n",
    "for i, num_basis  in enumerate([6, 10, 14]) :  \n",
    "    output_file_prefix=outdir + channel + '_para-dim-' + f'{dim_para}' \\\n",
    "    + '_basis-' + f'{num_basis}'+'_full-sample-' + f'{num_full}' + '_'\n",
    "    test_pc_list_ere_mesh_list, testinouthaull, ere_var_mesh_list  = \\\n",
    "                        map(res_dict[output_file_prefix].get, ['test_pc_list_ere_mesh_list', 'testinouthaull', 'ere_var_mesh_list'] )   \n",
    "    ere_mesh_list_1 = test_pc_list_ere_mesh_list[testinouthaull]\n",
    "    ere_mesh_list_2 = test_pc_list_ere_mesh_list[np.logical_not(testinouthaull)]\n",
    "    ere_var_mesh_list_1=ere_var_mesh_list[testinouthaull]\n",
    "    ere_var_mesh_list_2=ere_var_mesh_list[np.logical_not(testinouthaull)]    \n",
    "    ax[0,0].plot(E_pts, np.mean( np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_1[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_1) ]) , axis=0 ), label = r\"$N_b:$\"+f'{num_basis}',\n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[0,1].plot(E_pts, np.mean( np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_2[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_2) ]) , axis=0 ), label = r\"$N_b:$\"+f'{num_basis}',\n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[1,0].plot(E_pts, np.std(np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_1[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_1) ]) , axis=0 ),  label = r\"$N_b:$\"+f'{num_basis}' ,\n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[1,1].plot(E_pts, np.std(np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_2[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_2) ]) , axis=0 ),  label = r\"$N_b:$\"+f'{num_basis}',\n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "ax[0,0].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[0,1].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[1,0].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[1,1].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "fig.tight_layout()\n",
    "plt.savefig(outdir+'1S0_'+'interpolation_vs_extrapolation_rel_error_4dim.pdf', bbox_inches='tight')  \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For 3S1 channel <a id=\"plots_3S1\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 489.6x326.4 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for 3S1 channel in 2-dim space\n",
    "channel , dim_para,  num_full = '3S1', 2, 200 \n",
    "color_list= ['red', 'blue', 'black']  \n",
    "linestyle_list= ['--', '-', ':']\n",
    "fig, ax = plt.subplots(ncols=2, nrows=2, figsize=(3.4*2, 3.4*2*2/3), sharex=True, sharey=True) \n",
    "fig.suptitle('Relative error for NN'+r' ($^3S_1$)'+' scattering; varying '+r'$V_{0R}$, $V_{0t}$' , x=0.5, y= 1.02,  fontsize=12)\n",
    "\n",
    "ax[0,0].set_yscale('log')\n",
    "ax[0,0].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[0,0].set_title('Mean for interpolation', fontsize= 10)\n",
    "ax[0,1].set_yscale('log')\n",
    "ax[0,1].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[0,1].set_title('Mean for extrapolation', fontsize= 10)\n",
    "ax[1,0].set_yscale('log')\n",
    "ax[1,0].set_xlabel('E (MeV)', fontsize=10)\n",
    "ax[1,0].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[1,0].set_title('Std for interpolation', fontsize= 10)\n",
    "ax[1,1].set_yscale('log')\n",
    "ax[1,1].set_xlabel('E (MeV)', fontsize=10)\n",
    "ax[1,1].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[1,1].set_title('Std for extrapolation', fontsize= 10)\n",
    "########### with num_basis = [4, 6, 8] \n",
    "for i, num_basis  in enumerate([4,6,8]) :  \n",
    "    output_file_prefix=outdir + channel + '_para-dim-' + f'{dim_para}' \\\n",
    "    + '_basis-' + f'{num_basis}'+'_full-sample-' + f'{num_full}' + '_'\n",
    "    test_pc_list_ere_mesh_list, testinouthaull, ere_var_mesh_list  = \\\n",
    "                        map(res_dict[output_file_prefix].get, [ 'test_pc_list_ere_mesh_list', 'testinouthaull', 'ere_var_mesh_list'] )   \n",
    "    ere_mesh_list_1 = test_pc_list_ere_mesh_list[testinouthaull]\n",
    "    ere_mesh_list_2 = test_pc_list_ere_mesh_list[np.logical_not(testinouthaull)]\n",
    "    ere_var_mesh_list_1=ere_var_mesh_list[testinouthaull]\n",
    "    ere_var_mesh_list_2=ere_var_mesh_list[np.logical_not(testinouthaull)]    \n",
    "    ax[0,0].plot(E_pts, np.mean( np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_1[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_1) ]) , axis=0 ), label = r\"$N_b:$\"+f'{num_basis}',\n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[0,1].plot(E_pts, np.mean( np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_2[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_2) ]) , axis=0 ), label = r\"$N_b:$\"+f'{num_basis}', \n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[1,0].plot(E_pts, np.std(np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_1[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_1) ]) , axis=0 ),  label = r\"$N_b:$\"+f'{num_basis}',\n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[1,1].plot(E_pts, np.std(np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_2[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_2) ]) , axis=0 ),  label = r\"$N_b:$\"+f'{num_basis}', \n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "\n",
    "#ax[0,0].legend(fontsize=10)\n",
    "ax[0,0].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[0,1].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[1,0].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[1,1].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "fig.tight_layout()\n",
    "plt.savefig(outdir+'3S1_'+'interpolation_vs_extrapolation_rel_error.pdf', bbox_inches='tight')  \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 489.6x326.4 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for 3S1 channel in 4-dim space\n",
    "channel , dim_para,  num_full = '3S1', 4, 1000 \n",
    "color_list= ['red', 'blue', 'black']  \n",
    "linestyle_list= ['--', '-', ':']\n",
    "fig, ax = plt.subplots(ncols=2, nrows=2, figsize=(3.4*2, 3.4*2*2/3), sharex=True, sharey=True) \n",
    "fig.suptitle('Relative error for NN'+r' ($^3S_1$)'+' scattering; varying '+r'$V_{0R}$, $V_{0t}$, $\\kappa_R$, $\\kappa_t$' \n",
    "             , x=0.5, y= 1.02,  fontsize=12)\n",
    "\n",
    "ax[0,0].set_yscale('log')\n",
    "ax[0,0].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[0,0].set_title('Mean for interpolation', fontsize= 10)\n",
    "ax[0,1].set_yscale('log')\n",
    "ax[0,1].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[0,1].set_title('Mean for extrapolation', fontsize= 10)\n",
    "ax[1,0].set_yscale('log')\n",
    "ax[1,0].set_xlabel('E (MeV)', fontsize=10)\n",
    "ax[1,0].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[1,0].set_title('Std for interpolation', fontsize= 10)\n",
    "ax[1,1].set_yscale('log')\n",
    "ax[1,1].set_xlabel('E (MeV)', fontsize=10)\n",
    "ax[1,1].tick_params(bottom=True, top=True, left=True, right=True)\n",
    "ax[1,1].set_title('Std for extrapolation', fontsize= 10)\n",
    "########### with num_basis = [6, 9, 12] \n",
    "for i, num_basis  in enumerate([6, 10, 14]) :  \n",
    "    output_file_prefix=outdir + channel + '_para-dim-' + f'{dim_para}' \\\n",
    "    + '_basis-' + f'{num_basis}'+'_full-sample-' + f'{num_full}' + '_'\n",
    "    test_pc_list_ere_mesh_list, testinouthaull, ere_var_mesh_list  = \\\n",
    "                        map(res_dict[output_file_prefix].get, [ 'test_pc_list_ere_mesh_list', 'testinouthaull', 'ere_var_mesh_list'] )   \n",
    "    ere_mesh_list_1 = test_pc_list_ere_mesh_list[testinouthaull]\n",
    "    ere_mesh_list_2 = test_pc_list_ere_mesh_list[np.logical_not(testinouthaull)]\n",
    "    ere_var_mesh_list_1=ere_var_mesh_list[testinouthaull]\n",
    "    ere_var_mesh_list_2=ere_var_mesh_list[np.logical_not(testinouthaull)]    \n",
    "    ax[0,0].plot(E_pts, np.mean( np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_1[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_1) ]) , axis=0 ), label = r\"$N_b:$\"+f'{num_basis}',\n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[0,1].plot(E_pts, np.mean( np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_2[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_2) ]) , axis=0 ), label = r\"$N_b:$\"+f'{num_basis}',\n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[1,0].plot(E_pts, np.std(np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_1[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_1) ]) , axis=0 ),  label = r\"$N_b:$\"+f'{num_basis}' ,\n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "    ax[1,1].plot(E_pts, np.std(np.array( [ np.absolute(ere_mesh[1]/ere_var_mesh_list_2[i]-1) \n",
    "                    for i, ere_mesh in enumerate(ere_mesh_list_2) ]) , axis=0 ),  label = r\"$N_b:$\"+f'{num_basis}' ,\n",
    "                 color=color_list[i], linestyle=linestyle_list[i])\n",
    "\n",
    "#ax[0,0].legend(fontsize=10)\n",
    "ax[0,0].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[0,1].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[1,0].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "#ax[1,1].legend(loc='best', fontsize=10, ncol=3 , columnspacing=1, handlelength=1, handletextpad=0.5) \n",
    "fig.tight_layout()\n",
    "plt.savefig(outdir+'3S1_'+'interpolation_vs_extrapolation_rel_error_4dim.pdf', bbox_inches='tight')  \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}